{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Graphene\n",
"\n",
"This example demonstrates the calculations of density of states (DOS) and transmission values for a two-probe graphene.\n",
"\n",
"## Import Necessary Libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import junpy as jp\n",
"from junpy.factory import nanodcal\n",
"%config InlineBackend.figure_formats = ['svg']\n",
"%config InlineBackend.rc = {'font.size': 12}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load Device"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"filename = (\n",
" 'jpdataset/nanodcal/twoprobe_graphene/'\n",
" 'LDA_SP/sys_1x2/v0.00/NanodcalStructObject.mat')\n",
"device = nanodcal.load_nanodcal_device(filename)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculate Density of States\n",
"\n",
"Since graphene has a two-dimensional structure, we need to integrate the k-space. In this example, the transport direction is along the $y$ direction, so we integrate the k-space along the $x$ direction. The object `jp.SymmetryKspaceSampling((n1, n2, n3))` specifies the number of k-points to be used along the reciprocal lattice vectors $b_1$, $b_2$, and $b_3$, respectively. Note that these calculations become time-consuming due to the integration."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": [
"hide-output"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" JunPy version---------------------------: 0.15.0.post29+ga5b3260\n",
" Parallelization information\n",
" BLAS Vendor-----------------------------: MKL\n",
" Total number of MPI processes-----------: 1\n",
" OMP_NUM_THREADS-------------------------: 1\n",
" MKL_NUM_THREADS-------------------------: unset\n",
" OPENBLAS_NUM_THREADS--------------------: unset\n",
" Calculating density of states... (2024-08-15 21:11:44)\n",
" Device information\n",
" bias (mu2-mu1)--------------------------: 0.0\n",
" central.numberOfSites-------------------: 8\n",
" central.spinType------------------------: SpinType.CollinearSpin\n",
" lead1.numberOfSites---------------------: 8\n",
" lead1.spinType--------------------------: SpinType.CollinearSpin\n",
" lead1.direction-------------------------: -1\n",
" lead1.temperature-----------------------: 0.0\n",
" lead1.chemicalPotential-----------------: -0.0\n",
" lead2.numberOfSites---------------------: 8\n",
" lead2.spinType--------------------------: SpinType.CollinearSpin\n",
" lead2.direction-------------------------: -1\n",
" lead2.temperature-----------------------: 0.0\n",
" lead2.chemicalPotential-----------------: -0.0\n",
" Energy sampling\n",
" samplingName----------------------------: CustomSampling\n",
" range-----------------------------------: [-4.0000e+00, 4.0000e+00]\n",
" number----------------------------------: 81\n",
" K-space sampling\n",
" samplingName----------------------------: SymmetryKspaceSampling\n",
" gridNumber------------------------------: (101, 1, 1)\n",
" isTimeReversalSymmetry------------------: True\n",
" numReducedKpoints-----------------------: 51\n",
" Runtime message\n",
" Integrate over energy and k-space...\n",
" Start MPI execution...\n",
" --> 5.0% finished (Elapsed time: 0:01:00.934257)\n",
" --> 10.0% finished (Elapsed time: 0:01:03.760330)\n",
" --> 15.0% finished (Elapsed time: 0:00:58.744127)\n",
" --> 20.0% finished (Elapsed time: 0:01:05.659762)\n",
" --> 25.1% finished (Elapsed time: 0:00:59.667289)\n",
" --> 30.1% finished (Elapsed time: 0:01:07.333848)\n",
" --> 35.1% finished (Elapsed time: 0:01:05.513847)\n",
" --> 40.1% finished (Elapsed time: 0:01:11.569475)\n",
" --> 45.1% finished (Elapsed time: 0:01:11.459732)\n",
" --> 50.1% finished (Elapsed time: 0:01:14.092089)\n",
" --> 55.1% finished (Elapsed time: 0:01:14.757715)\n",
" --> 60.1% finished (Elapsed time: 0:01:15.730488)\n",
" --> 65.1% finished (Elapsed time: 0:01:18.600627)\n",
" --> 70.1% finished (Elapsed time: 0:01:19.798855)\n",
" --> 75.1% finished (Elapsed time: 0:01:14.960501)\n",
" --> 80.1% finished (Elapsed time: 0:01:05.175154)\n",
" --> 85.0% finished (Elapsed time: 0:01:02.974258)\n",
" --> 90.0% finished (Elapsed time: 0:00:54.497405)\n",
" --> 95.0% finished (Elapsed time: 0:00:44.964707)\n",
" --> 100.0% finished (Elapsed time: 0:00:41.109262)\n",
" Wait for other processes...\n",
" --> finished (Elapsed time: 0:00:00.000055)\n",
" Gather results from other processes...\n",
" --> finished (Elapsed time: 0:00:00.000433)\n",
" Density of states report\n",
" Energy_eV D_up D_dn\n",
" -4.000000e+00 1.148054e+00 1.148054e+00\n",
" -3.900000e+00 1.151423e+00 1.151423e+00\n",
" -3.800000e+00 1.137059e+00 1.137059e+00\n",
" -3.700000e+00 1.125215e+00 1.125216e+00\n",
" -3.600000e+00 1.138127e+00 1.138127e+00\n",
" -3.500000e+00 1.114009e+00 1.114010e+00\n",
" -3.400000e+00 1.114928e+00 1.114928e+00\n",
" -3.300000e+00 1.119039e+00 1.119040e+00\n",
" -3.200000e+00 1.086117e+00 1.086118e+00\n",
" -3.100000e+00 1.053182e+00 1.053183e+00\n",
" -3.000000e+00 8.547575e-01 8.547585e-01\n",
" -2.900000e+00 8.178881e-01 8.178885e-01\n",
" -2.800000e+00 8.465649e-01 8.465660e-01\n",
" -2.700000e+00 8.562368e-01 8.562372e-01\n",
" -2.600000e+00 9.347888e-01 9.347900e-01\n",
" -2.500000e+00 1.004012e+00 1.004014e+00\n",
" -2.400000e+00 1.163116e+00 1.163114e+00\n",
" -2.300000e+00 1.053529e+00 1.053528e+00\n",
" -2.200000e+00 8.438950e-01 8.438942e-01\n",
" -2.100000e+00 7.796125e-01 7.796106e-01\n",
" -2.000000e+00 6.949276e-01 6.949277e-01\n",
" -1.900000e+00 6.103559e-01 6.103555e-01\n",
" -1.800000e+00 5.885922e-01 5.885915e-01\n",
" -1.700000e+00 5.187629e-01 5.187628e-01\n",
" -1.600000e+00 4.864822e-01 4.864817e-01\n",
" -1.500000e+00 4.502752e-01 4.502751e-01\n",
" -1.400000e+00 4.061107e-01 4.061105e-01\n",
" -1.300000e+00 3.899114e-01 3.899112e-01\n",
" -1.200000e+00 3.484829e-01 3.484829e-01\n",
" -1.100000e+00 3.245921e-01 3.245920e-01\n",
" -1.000000e+00 3.007624e-01 3.007624e-01\n",
" -9.000000e-01 2.682955e-01 2.682955e-01\n",
" -8.000000e-01 2.522408e-01 2.522408e-01\n",
" -7.000000e-01 2.253794e-01 2.253794e-01\n",
" -6.000000e-01 2.024319e-01 2.024319e-01\n",
" -5.000000e-01 1.870288e-01 1.870289e-01\n",
" -4.000000e-01 1.612114e-01 1.612115e-01\n",
" -3.000000e-01 1.396932e-01 1.396933e-01\n",
" -2.000000e-01 1.242044e-01 1.242045e-01\n",
" -1.000000e-01 1.066135e-01 1.066137e-01\n",
" 0.000000e+00 9.609875e-02 9.609895e-02\n",
" 1.000000e-01 1.080408e-01 1.080410e-01\n",
" 2.000000e-01 1.269432e-01 1.269434e-01\n",
" 3.000000e-01 1.444241e-01 1.444243e-01\n",
" 4.000000e-01 1.673718e-01 1.673721e-01\n",
" 5.000000e-01 1.963720e-01 1.963724e-01\n",
" 6.000000e-01 2.168159e-01 2.168163e-01\n",
" 7.000000e-01 2.431098e-01 2.431101e-01\n",
" 8.000000e-01 2.775946e-01 2.775951e-01\n",
" 9.000000e-01 2.988199e-01 2.988204e-01\n",
" 1.000000e+00 3.386903e-01 3.386908e-01\n",
" 1.100000e+00 3.786392e-01 3.786400e-01\n",
" 1.200000e+00 4.095431e-01 4.095436e-01\n",
" 1.300000e+00 4.800447e-01 4.800454e-01\n",
" 1.400000e+00 5.191383e-01 5.191394e-01\n",
" 1.500000e+00 5.985113e-01 5.985117e-01\n",
" 1.600000e+00 7.375083e-01 7.375099e-01\n",
" 1.700000e+00 8.671765e-01 8.671788e-01\n",
" 1.800000e+00 1.168567e+00 1.168570e+00\n",
" 1.900000e+00 1.164942e+00 1.164942e+00\n",
" 2.000000e+00 9.781349e-01 9.781341e-01\n",
" 2.100000e+00 8.786198e-01 8.786194e-01\n",
" 2.200000e+00 8.067168e-01 8.067164e-01\n",
" 2.300000e+00 7.693844e-01 7.693842e-01\n",
" 2.400000e+00 7.215649e-01 7.215648e-01\n",
" 2.500000e+00 7.054427e-01 7.054426e-01\n",
" 2.600000e+00 6.672415e-01 6.672415e-01\n",
" 2.700000e+00 6.606485e-01 6.606483e-01\n",
" 2.800000e+00 6.281496e-01 6.281497e-01\n",
" 2.900000e+00 6.263867e-01 6.263866e-01\n",
" 3.000000e+00 5.977874e-01 5.977875e-01\n",
" 3.100000e+00 5.987021e-01 5.987020e-01\n",
" 3.200000e+00 5.728537e-01 5.728538e-01\n",
" 3.300000e+00 5.756030e-01 5.756029e-01\n",
" 3.400000e+00 5.516298e-01 5.516299e-01\n",
" 3.500000e+00 5.558199e-01 5.558198e-01\n",
" 3.600000e+00 5.331058e-01 5.331059e-01\n",
" 3.700000e+00 5.383876e-01 5.383876e-01\n",
" 3.800000e+00 5.166774e-01 5.166776e-01\n",
" 3.900000e+00 5.226148e-01 5.226148e-01\n",
" 4.000000e+00 5.022855e-01 5.022856e-01\n",
" Calculation of density of states finished (2024-08-15 21:33:35)\n",
" Elapsed time----------------------------: 0:21:51.487874\n"
]
}
],
"source": [
"calcr_dos = jp.DensityOfStates(\n",
" device=device,\n",
" energies=np.linspace(-4, 4, 81),\n",
" kpoints=jp.SymmetryKspaceSampling((101,1,1)),\n",
" etaSigma=0.05,\n",
" etaGF=0.05)\n",
"jp.run(calcr_dos, savefile=False)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# shape: (#kpoints, #energies, #spin)\n",
"dos = calcr_dos.densityOfStates(spin='sum')\n",
"\n",
"plt.plot(calcr_dos.energies, dos[0,:,0], '.-')\n",
"plt.xlabel('Energy (eV)')\n",
"plt.ylabel('DOS (1/eV)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculate Transmission"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"tags": [
"hide-output"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" JunPy version---------------------------: 0.15.0.post29+ga5b3260\n",
" Parallelization information\n",
" BLAS Vendor-----------------------------: MKL\n",
" Total number of MPI processes-----------: 1\n",
" OMP_NUM_THREADS-------------------------: 1\n",
" MKL_NUM_THREADS-------------------------: unset\n",
" OPENBLAS_NUM_THREADS--------------------: unset\n",
" Calculating transmission... (2024-08-15 21:54:34)\n",
" Device information\n",
" bias (mu2-mu1)--------------------------: 0.0\n",
" central.numberOfSites-------------------: 8\n",
" central.spinType------------------------: SpinType.CollinearSpin\n",
" lead1.numberOfSites---------------------: 8\n",
" lead1.spinType--------------------------: SpinType.CollinearSpin\n",
" lead1.direction-------------------------: -1\n",
" lead1.temperature-----------------------: 0.0\n",
" lead1.chemicalPotential-----------------: -0.0\n",
" lead2.numberOfSites---------------------: 8\n",
" lead2.spinType--------------------------: SpinType.CollinearSpin\n",
" lead2.direction-------------------------: -1\n",
" lead2.temperature-----------------------: 0.0\n",
" lead2.chemicalPotential-----------------: -0.0\n",
" Energy sampling\n",
" samplingName----------------------------: CustomSampling\n",
" range-----------------------------------: [-4.0000e+00, 4.0000e+00]\n",
" number----------------------------------: 81\n",
" K-space sampling\n",
" samplingName----------------------------: SymmetryKspaceSampling\n",
" gridNumber------------------------------: (101, 1, 1)\n",
" isTimeReversalSymmetry------------------: True\n",
" numReducedKpoints-----------------------: 51\n",
" Runtime message\n",
" Integrate over energy and k-space...\n",
" Start MPI execution...\n",
" --> 5.0% finished (Elapsed time: 0:01:01.678480)\n",
" --> 10.0% finished (Elapsed time: 0:01:05.354264)\n",
" --> 15.0% finished (Elapsed time: 0:00:59.842669)\n",
" --> 20.0% finished (Elapsed time: 0:01:07.359267)\n",
" --> 25.1% finished (Elapsed time: 0:01:01.623016)\n",
" --> 30.1% finished (Elapsed time: 0:01:09.152400)\n",
" --> 35.1% finished (Elapsed time: 0:01:05.336416)\n",
" --> 40.1% finished (Elapsed time: 0:01:10.703299)\n",
" --> 45.1% finished (Elapsed time: 0:01:10.825140)\n",
" --> 50.1% finished (Elapsed time: 0:01:11.762769)\n",
" --> 55.1% finished (Elapsed time: 0:01:11.643890)\n",
" --> 60.1% finished (Elapsed time: 0:01:12.286803)\n",
" --> 65.1% finished (Elapsed time: 0:01:15.848238)\n",
" --> 70.1% finished (Elapsed time: 0:01:16.276325)\n",
" --> 75.1% finished (Elapsed time: 0:01:11.613738)\n",
" --> 80.1% finished (Elapsed time: 0:01:02.647705)\n",
" --> 85.0% finished (Elapsed time: 0:00:59.451811)\n",
" --> 90.0% finished (Elapsed time: 0:00:51.418889)\n",
" --> 95.0% finished (Elapsed time: 0:00:45.719981)\n",
" --> 100.0% finished (Elapsed time: 0:00:41.742144)\n",
" Wait for other processes...\n",
" --> finished (Elapsed time: 0:00:00.000025)\n",
" Gather results from other processes...\n",
" --> finished (Elapsed time: 0:00:00.000246)\n",
" Transmission report\n",
" Energy_eV T_up T_dn\n",
" -4.000000e+00 1.122606e+00 1.122607e+00\n",
" -3.900000e+00 1.104640e+00 1.104641e+00\n",
" -3.800000e+00 1.082771e+00 1.082771e+00\n",
" -3.700000e+00 1.062135e+00 1.062136e+00\n",
" -3.600000e+00 1.038053e+00 1.038053e+00\n",
" -3.500000e+00 1.010902e+00 1.010902e+00\n",
" -3.400000e+00 9.812795e-01 9.812797e-01\n",
" -3.300000e+00 9.431727e-01 9.431729e-01\n",
" -3.200000e+00 8.981820e-01 8.981822e-01\n",
" -3.100000e+00 8.352657e-01 8.352660e-01\n",
" -3.000000e+00 7.873350e-01 7.873350e-01\n",
" -2.900000e+00 7.912590e-01 7.912590e-01\n",
" -2.800000e+00 7.947095e-01 7.947095e-01\n",
" -2.700000e+00 7.982991e-01 7.982991e-01\n",
" -2.600000e+00 7.971223e-01 7.971223e-01\n",
" -2.500000e+00 7.875332e-01 7.875331e-01\n",
" -2.400000e+00 7.491970e-01 7.491967e-01\n",
" -2.300000e+00 6.577973e-01 6.577971e-01\n",
" -2.200000e+00 5.979276e-01 5.979275e-01\n",
" -2.100000e+00 5.519077e-01 5.519076e-01\n",
" -2.000000e+00 5.133411e-01 5.133409e-01\n",
" -1.900000e+00 4.790098e-01 4.790097e-01\n",
" -1.800000e+00 4.461595e-01 4.461594e-01\n",
" -1.700000e+00 4.173484e-01 4.173483e-01\n",
" -1.600000e+00 3.870860e-01 3.870859e-01\n",
" -1.500000e+00 3.610186e-01 3.610185e-01\n",
" -1.400000e+00 3.336284e-01 3.336283e-01\n",
" -1.300000e+00 3.079797e-01 3.079795e-01\n",
" -1.200000e+00 2.834143e-01 2.834142e-01\n",
" -1.100000e+00 2.568344e-01 2.568343e-01\n",
" -1.000000e+00 2.344523e-01 2.344522e-01\n",
" -9.000000e-01 2.087767e-01 2.087766e-01\n",
" -8.000000e-01 1.845871e-01 1.845871e-01\n",
" -7.000000e-01 1.622581e-01 1.622581e-01\n",
" -6.000000e-01 1.372000e-01 1.372000e-01\n",
" -5.000000e-01 1.166885e-01 1.166884e-01\n",
" -4.000000e-01 9.448405e-02 9.448401e-02\n",
" -3.000000e-01 6.905113e-02 6.905110e-02\n",
" -2.000000e-01 4.829559e-02 4.829556e-02\n",
" -1.000000e-01 2.948585e-02 2.948583e-02\n",
" 0.000000e+00 1.341752e-02 1.341752e-02\n",
" 1.000000e-01 2.984253e-02 2.984255e-02\n",
" 2.000000e-01 4.859666e-02 4.859669e-02\n",
" 3.000000e-01 6.983141e-02 6.983144e-02\n",
" 4.000000e-01 9.539847e-02 9.539850e-02\n",
" 5.000000e-01 1.188249e-01 1.188250e-01\n",
" 6.000000e-01 1.401512e-01 1.401513e-01\n",
" 7.000000e-01 1.653895e-01 1.653895e-01\n",
" 8.000000e-01 1.889342e-01 1.889343e-01\n",
" 9.000000e-01 2.136815e-01 2.136816e-01\n",
" 1.000000e+00 2.411958e-01 2.411959e-01\n",
" 1.100000e+00 2.667825e-01 2.667826e-01\n",
" 1.200000e+00 2.963932e-01 2.963933e-01\n",
" 1.300000e+00 3.259322e-01 3.259323e-01\n",
" 1.400000e+00 3.600282e-01 3.600284e-01\n",
" 1.500000e+00 3.992933e-01 3.992935e-01\n",
" 1.600000e+00 4.469148e-01 4.469151e-01\n",
" 1.700000e+00 5.130348e-01 5.130351e-01\n",
" 1.800000e+00 6.278325e-01 6.278330e-01\n",
" 1.900000e+00 7.970361e-01 7.970365e-01\n",
" 2.000000e+00 8.415783e-01 8.415785e-01\n",
" 2.100000e+00 8.579623e-01 8.579624e-01\n",
" 2.200000e+00 8.621175e-01 8.621175e-01\n",
" 2.300000e+00 8.645284e-01 8.645284e-01\n",
" 2.400000e+00 8.619564e-01 8.619564e-01\n",
" 2.500000e+00 8.599122e-01 8.599122e-01\n",
" 2.600000e+00 8.550602e-01 8.550602e-01\n",
" 2.700000e+00 8.506707e-01 8.506707e-01\n",
" 2.800000e+00 8.448290e-01 8.448290e-01\n",
" 2.900000e+00 8.391019e-01 8.391018e-01\n",
" 3.000000e+00 8.327214e-01 8.327213e-01\n",
" 3.100000e+00 8.262044e-01 8.262043e-01\n",
" 3.200000e+00 8.194786e-01 8.194785e-01\n",
" 3.300000e+00 8.125040e-01 8.125039e-01\n",
" 3.400000e+00 8.054545e-01 8.054545e-01\n",
" 3.500000e+00 7.983186e-01 7.983186e-01\n",
" 3.600000e+00 7.908719e-01 7.908719e-01\n",
" 3.700000e+00 7.838249e-01 7.838249e-01\n",
" 3.800000e+00 7.759028e-01 7.759027e-01\n",
" 3.900000e+00 7.694953e-01 7.694952e-01\n",
" 4.000000e+00 7.609718e-01 7.609718e-01\n",
" Calculation of transmission finished (2024-08-15 22:16:07)\n",
" Elapsed time----------------------------: 0:21:32.510540\n"
]
}
],
"source": [
"calcr_trans = jp.Transmission(\n",
" device=device,\n",
" energies=np.linspace(-4, 4, 81),\n",
" kpoints=jp.SymmetryKspaceSampling((101,1,1)),\n",
" etaSigma=0.05,\n",
" etaGF=0.05)\n",
"jp.run(calcr_trans, savefile=False)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# shape: (#kpoints, #energies, #spin)\n",
"trans = calcr_trans.transmission(spin='sum')\n",
"\n",
"plt.plot(calcr_trans.energies, trans[0,:,0], '.-')\n",
"plt.xlabel('Energy (eV)')\n",
"plt.ylabel('Transmission')\n",
"plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "junpy",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.13"
}
},
"nbformat": 4,
"nbformat_minor": 2
}